Update: For completeness's sake, it might be worth noting that on CPAN you can find String::Util, which includes a function called trim() that does exactly what you're talking about. ...it's been done. ;)

I think the alternation in the s/^\s+|\s+$// version causes significant time costs in large applications. I often work with tab-delimited files containing hundreds of thousands of lines. If I'm tab-splitting these lines and then trimming each one, I'm going to pick the double-regex approach each time.
I wrote some quick code that benchmarked the double-regex vs single-regex approach against three strings.

That's after only 1,000,000 trims. In a 800,000 line file with 50 columns per line, we're talking about 40,000,000 trims. Assuming a linear scale, that means I give up about a minute of processing time per file per run. That's far less than the time it would have taken me to type two regexes.
Admittedly, it's a small optimization, and only valid for those who are processing files on the scale that I do, but for most people who end up typing the 'trim regex' often enough to complain about it on perlmonks, it probably applies.